A Sparsity Adaptive Greedy Iterative Algorithm for Compressed Sensing

Aiming at the problem of signal reconstruction with unknown sparsity in compressed sensing, an improved iterative greedy algorithm is proposed to signal reconstruction from low sampling rate. Firstly, a sparsity estimation strategy is used to estimate the sparsity and the true support set of target signal, and then the residual is initialized with the estimated value. In order to optimize the estimated value, it is necessary to determine the direction of the iteration before the iteration begins. The proposed algorithm is associated with the ideas of adaptive, backtracking and greedy choice to iteratively refine. The simulation results show that the proposed algorithm performs better than that of OMP, CoSaMP and SAMP algorithms for both one-dimensional signal and two-dimensional image signal, and the algorithm has better practical application value.

[1]  Damiana Lazzaro,et al.  A Fast Compressed Sensing Approach to 3D MR Image Reconstruction , 2011, IEEE Transactions on Medical Imaging.

[2]  Jian Liu,et al.  A novel signal separation algorithm based on compressed sensing for wideband spectrum sensing in cognitive radio networks , 2014, Int. J. Commun. Syst..

[3]  Yonina C. Eldar,et al.  From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals , 2009, IEEE Journal of Selected Topics in Signal Processing.

[4]  Jianwu Dang,et al.  Image decomposing for inpainting using compressed sensing in DCT domain , 2014, Frontiers of Computer Science.

[5]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

[6]  Marco Martorella,et al.  Compressive sensing-based inverse synthetic radar imaging imaging from incomplete data , 2016 .

[7]  Richard H. Sherman,et al.  Chaotic communications in the presence of noise , 1993, Optics & Photonics.

[8]  Yahong Rosa Zheng,et al.  Compressed sensing for SAR-based wideband three-dimensional microwave imaging system using non-uniform fast fourier transform , 2013 .

[9]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[10]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[11]  Massoud Babaie-Zadeh,et al.  Compressive detection of sparse signals in additive white Gaussian noise without signal reconstruction , 2017, Signal Process..

[12]  Graham Cormode,et al.  Combinatorial Algorithms for Compressed Sensing , 2006 .

[13]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[14]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[15]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[16]  Thong T. Do,et al.  Sparsity adaptive matching pursuit algorithm for practical compressed sensing , 2008, 2008 42nd Asilomar Conference on Signals, Systems and Computers.

[17]  Zhai Guangjie,et al.  Super-resolution ghost imaging via compressed sensing , 2014 .

[18]  Miki Haseyama,et al.  Random combination for information extraction in compressed sensing and sparse representation-based pattern recognition , 2014, Neurocomputing.